Question

How to know that an integration should be solved by parts just by looking at the question?

Answer 1

Integration by parts can be used when the integrand of the integration is product of two different kind of functions. Suppose one function is polynomial and other is trigonometric or one function is polynomial and other functions is logarithmic/ exponential like that it can have different combinations. Sometimes integrand is not given in directly in product form but by some algebraic manipulation it can be separated out in two functions.

To choose first function (u) we usually follow the rule of ILATE.

I - Inverse Trigonometric Function

L - Logarithm Function

A - Algebraic Function

T - Trigonometric Function

E - Exponential Function .

After choosing first function (u) the other function will be by default v.